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      SUBROUTINE <a name="DPTTRF.1"></a><a href="dpttrf.f.html#DPTTRF.1">DPTTRF</a>( N, D, E, INFO )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  -- LAPACK routine (version 3.1) --
</span><span class="comment">*</span><span class="comment">     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
</span><span class="comment">*</span><span class="comment">     November 2006
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     .. Scalar Arguments ..
</span>      INTEGER            INFO, N
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Array Arguments ..
</span>      DOUBLE PRECISION   D( * ), E( * )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Purpose
</span><span class="comment">*</span><span class="comment">  =======
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  <a name="DPTTRF.17"></a><a href="dpttrf.f.html#DPTTRF.1">DPTTRF</a> computes the L*D*L' factorization of a real symmetric
</span><span class="comment">*</span><span class="comment">  positive definite tridiagonal matrix A.  The factorization may also
</span><span class="comment">*</span><span class="comment">  be regarded as having the form A = U'*D*U.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Arguments
</span><span class="comment">*</span><span class="comment">  =========
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  N       (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The order of the matrix A.  N &gt;= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  D       (input/output) DOUBLE PRECISION array, dimension (N)
</span><span class="comment">*</span><span class="comment">          On entry, the n diagonal elements of the tridiagonal matrix
</span><span class="comment">*</span><span class="comment">          A.  On exit, the n diagonal elements of the diagonal matrix
</span><span class="comment">*</span><span class="comment">          D from the L*D*L' factorization of A.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  E       (input/output) DOUBLE PRECISION array, dimension (N-1)
</span><span class="comment">*</span><span class="comment">          On entry, the (n-1) subdiagonal elements of the tridiagonal
</span><span class="comment">*</span><span class="comment">          matrix A.  On exit, the (n-1) subdiagonal elements of the
</span><span class="comment">*</span><span class="comment">          unit bidiagonal factor L from the L*D*L' factorization of A.
</span><span class="comment">*</span><span class="comment">          E can also be regarded as the superdiagonal of the unit
</span><span class="comment">*</span><span class="comment">          bidiagonal factor U from the U'*D*U factorization of A.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  INFO    (output) INTEGER
</span><span class="comment">*</span><span class="comment">          = 0: successful exit
</span><span class="comment">*</span><span class="comment">          &lt; 0: if INFO = -k, the k-th argument had an illegal value
</span><span class="comment">*</span><span class="comment">          &gt; 0: if INFO = k, the leading minor of order k is not
</span><span class="comment">*</span><span class="comment">               positive definite; if k &lt; N, the factorization could not
</span><span class="comment">*</span><span class="comment">               be completed, while if k = N, the factorization was
</span><span class="comment">*</span><span class="comment">               completed, but D(N) &lt;= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  =====================================================================
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     .. Parameters ..
</span>      DOUBLE PRECISION   ZERO
      PARAMETER          ( ZERO = 0.0D+0 )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Local Scalars ..
</span>      INTEGER            I, I4
      DOUBLE PRECISION   EI
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Subroutines ..
</span>      EXTERNAL           <a name="XERBLA.58"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Intrinsic Functions ..
</span>      INTRINSIC          MOD
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Executable Statements ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Test the input parameters.
</span><span class="comment">*</span><span class="comment">
</span>      INFO = 0
      IF( N.LT.0 ) THEN
         INFO = -1
         CALL <a name="XERBLA.70"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>( <span class="string">'<a name="DPTTRF.70"></a><a href="dpttrf.f.html#DPTTRF.1">DPTTRF</a>'</span>, -INFO )
         RETURN
      END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Quick return if possible
</span><span class="comment">*</span><span class="comment">
</span>      IF( N.EQ.0 )
     $   RETURN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Compute the L*D*L' (or U'*D*U) factorization of A.
</span><span class="comment">*</span><span class="comment">
</span>      I4 = MOD( N-1, 4 )
      DO 10 I = 1, I4
         IF( D( I ).LE.ZERO ) THEN
            INFO = I
            GO TO 30
         END IF
         EI = E( I )
         E( I ) = EI / D( I )
         D( I+1 ) = D( I+1 ) - E( I )*EI
   10 CONTINUE
<span class="comment">*</span><span class="comment">
</span>      DO 20 I = I4 + 1, N - 4, 4
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Drop out of the loop if d(i) &lt;= 0: the matrix is not positive
</span><span class="comment">*</span><span class="comment">        definite.
</span><span class="comment">*</span><span class="comment">
</span>         IF( D( I ).LE.ZERO ) THEN
            INFO = I
            GO TO 30
         END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Solve for e(i) and d(i+1).
</span><span class="comment">*</span><span class="comment">
</span>         EI = E( I )
         E( I ) = EI / D( I )
         D( I+1 ) = D( I+1 ) - E( I )*EI
<span class="comment">*</span><span class="comment">
</span>         IF( D( I+1 ).LE.ZERO ) THEN
            INFO = I + 1
            GO TO 30
         END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Solve for e(i+1) and d(i+2).
</span><span class="comment">*</span><span class="comment">
</span>         EI = E( I+1 )
         E( I+1 ) = EI / D( I+1 )
         D( I+2 ) = D( I+2 ) - E( I+1 )*EI
<span class="comment">*</span><span class="comment">
</span>         IF( D( I+2 ).LE.ZERO ) THEN
            INFO = I + 2
            GO TO 30
         END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Solve for e(i+2) and d(i+3).
</span><span class="comment">*</span><span class="comment">
</span>         EI = E( I+2 )
         E( I+2 ) = EI / D( I+2 )
         D( I+3 ) = D( I+3 ) - E( I+2 )*EI
<span class="comment">*</span><span class="comment">
</span>         IF( D( I+3 ).LE.ZERO ) THEN
            INFO = I + 3
            GO TO 30
         END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Solve for e(i+3) and d(i+4).
</span><span class="comment">*</span><span class="comment">
</span>         EI = E( I+3 )
         E( I+3 ) = EI / D( I+3 )
         D( I+4 ) = D( I+4 ) - E( I+3 )*EI
   20 CONTINUE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Check d(n) for positive definiteness.
</span><span class="comment">*</span><span class="comment">
</span>      IF( D( N ).LE.ZERO )
     $   INFO = N
<span class="comment">*</span><span class="comment">
</span>   30 CONTINUE
      RETURN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     End of <a name="DPTTRF.150"></a><a href="dpttrf.f.html#DPTTRF.1">DPTTRF</a>
</span><span class="comment">*</span><span class="comment">
</span>      END

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